Besides ANCOVA's statistical inability to generate unbiased
adjusted means when intact groups are compared, there is a second, logical
reason why you should be on guard whenever you come across a research
report in which ANCOVA was used in an effort to "equate" intact
groups. Simply stated, the covariate variable(s) used by the researcher
may not address one or more important differences between the intact groups.
In Excerpt 18.24 [not shown here], for example, the researchers realized
that their intact groups might have been different to begin with. Consequently,
they covaried on GPA "to control for academic differences."
However, it is debatable whether academic differences among people are
reflected totally in their GPAs, and it is even more debatable whether
academic differences alone influence recall. In this and many other studies,
people's motivation plays no small part in how well they perform!

In summary, be extremely cautious when confronted with
research claims based upon the use of ANCOVA with intact groups. If an
important covariate variable was overlooked by those who conducted the
study, pay no attention whatsoever to the conclusions based upon the data
analysis. Even in the case where data on all important covariate variables
were collected and used you still should be tentative
in your inclination to "buy into" the claims made by the researchers.